In algebra, an elliptic algebra is a certain regular algebra of a Gelfand–Kirillov dimension three (quantum polynomial ring in three variables) that corresponds...

mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined...

produce 3D vector space and elliptic space, respectively. Access to elliptic space structure is provided through the vector algebra of William Rowan Hamilton:...

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC...

Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

In algebraic geometry, supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p > 0 {\displaystyle p>0} with...

mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such...

most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves...

theorem Elliptic surface Surface of general type Zariski surface Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension of an algebraic variety...

In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This...

(isomorphism classes of) certain algebraic objects called Sullivan minimal models, which are commutative differential graded algebras over the rational numbers...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

function field associated with the elliptic curve. A generalization of the Hasse bound to higher genus algebraic curves is the Hasse–Weil bound. This...

and the set of versors is a 3-sphere in the 4-dimensional quaternion algebra. Hamilton denoted the versor of a quaternion q by the symbol U q. He was...

mathematics, the Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional...

In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

geometry. The group SL(2, R) acts on its Lie algebra sl(2, R) by conjugation (remember that the Lie algebra elements are also 2 × 2 matrices), yielding...

{\displaystyle G_{6}} are so called Eisenstein series. In algebraic language, the field of elliptic functions is isomorphic to the field C ( X ) [ Y ] / (...

The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer...

A one-dimensional Calabi–Yau manifold is a complex elliptic curve, and in particular, algebraic. In two complex dimensions, the K3 surfaces furnish the...

metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement...

the elliptic rational function. ζ n {\displaystyle \zeta _{n}} is expressible for all n in terms of Jacobi elliptic functions, or algebraically for some...

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in...

Legendre's trigonometric form of the elliptic integral; substituting t = sin θ and x = sin φ, one obtains Jacobi's algebraic form: F ( x ; k ) = ∫ 0 x d t (...

of elliptic curves over the complex numbers, or more generally, an algebraically closed field. Over other fields there exist examples of elliptic curves...

group on Minkowski space uses biquaternions, which form a composition algebra. The isometry property of Lorentz transformations holds according to the...

two manuscripts, "Modular elliptic curves and Fermat's Last Theorem" and "Ring theoretic properties of certain Hecke algebras", the second of which Wiles...

trigonometric and elliptic. These are related to quantum groups known as the Yangian, affine quantum groups and elliptic algebras respectively. Set-theoretic...